hi Sue, you can buy anti slip underlay. Look out for the sort that works with carpet - much of what is sold is for wood/laminate floors. I bought some years ago and it is wonderful.
They make a type of carpet tape for sticking carpet on carpet, I use it all the time in my work. Its yellow and looks like a web of sticky threads, I get it in carpet departments of every home store I've been in. You can easily remove it and it doesn't leave behind a sticky mess. Sorry I don't know the name but its about 2 1/2" wide. Rug gripper is another brand that I have not used.